Can you statistically compare one subset of a population with the whole population? I have data (total $n=90$) from a district of testing scores from $3$ subsequent years.  I would like to compare my school to the other schools, but I do not know which schools the other participants come from.  In other words, I do not know which school the $90$ children go to, except my $10-12$ students.
In addition, I have scores from Math, English, Social Studies, Science, and an overall score.
How would I set up this data to compare the scores? I would like to compare my school to others for $3$ years in all areas.
 A: The data is usually organized by placing each variable value along a column and each individual (student) in a row. I'm assuming that each student was only evaluated once.
The variables could start with student ID (e.g., 1,2,3,...), year, school (that can be coded as 1 for school A, 2 for school B, etc.), Math grade, English grade, Social Studies grade, Science grade, and Overall Score.
If you know how to use a spreadsheet program this should be easy to do, and before you start putting data on your database, don't forget to use the first line to write the names of the variables. It will be even better if you know how to use some statistics software.
To start with, you could compute the mean and the standard deviation for each school and for each grade. This would give you some feeling on what is going on with the data. I.e., which school has the highest grade on Math, or which school has the highest grade in English.
If you want to do some statistical tests, you could start by evaluating the normality of each variable. Then, since you want to compare several independent groups (the schools) you should use an ANOVA (if that variable follows approximately a normal distribution) or the Kruskal-Wallis test (if that variable does not follow a normal distribution). The ANOVA tests will compare the means between the schools, while the Kruskal-Wallis tests compares the distributions between schools, but you can use the median grade of each school to visualise the differences.
To raise the complexity one step further, and assuming that the normality of the grades can be assumed, you can do a MANOVA, using as dependent variables all the grades (eventually with the exception of the Overall Score, if it is just a function of the other grades) and using as independent factors the school and the year (I'm assuming that there is not a monotonous relation between the year and each grade). With this test you can observe not only if there are differences between schools, but also if there are differences between the years.
I tried to present several ways of analysing the data, with different levels of difficulty.
